Application of Fuzzy System in Psychological Tests ... · Application of Fuzzy System in...

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IPA International Journal of Psychology Vol. 9, No. 2, Summer & Fall 2015

PP. 51-75

Iranian Psychological

Association

Application of Fuzzy System in Psychological Tests: Optimize the Number of Questions

for WHOQOL-BREF

Hamid Reza Ghanbari* Department of psychology

University of Sistan and Baluchestan

Mehrdad Mazaheri, PhD Department of psychology

Ferdowsi University of Mashhad University of Sistan and Baluchestan

Hasan Mishmast nehi, PhD Department of mathematics

University of Sistan and Baluchestan

The WHOQOL-BREF is one of the best known questionnaires for measuring the quality of life. It is currently available in more than 40 languages and has been used frequently in cross-cultural comparison studies on subjective well-being and quality of life studies. Some research shows that due to certaincultural biases Iranian respondentshave no tendency or willingness to responding some questions, more specially, question 21, in WHOQOL-BREF. The main aim of the current research was to use the ability and flexibility of fuzzy systems to analyse the WHOQOL-BREF questions to reduce some unclear or doubtful questions. A fuzzy system model proposes to diminish the errors that produce ambiguous concepts by not responding to certain biased questions.The WHOQOL-BREEquestionnaire was analyzed and both the traditional model and the fuzzy model analyses were compared for results using fuzzy systems.As a result, question 21 was removed from the WHOQOL-BREF questionnaire used by the fuzzy system. Keyword: WHOQOL-BREF, psychological test, fuzzy system, Wang & Mandel method, Quality Of Life, Cultural Bias

The theoretical definitions of the “quality of life” and some

related concepts such as “well–being”, “ happiness”, “ life

satisfaction” and “good life” have preoccupied a wide range of

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disciplines, dating as far back asAristotle (384-19 BC) and early

Greek philosophy (Bowling, 2001). Aristotle, using the Greek

eudaimonia ( a concept which for Aristotle meant having an

understanding of the best way to live one’s life), whichis

commonly translated as ‘happiness’, affirms that the quality of

life is highly relative: it means different things to different

people, and conditions for happiness vary according to a

person’s current condition. Happiness for Aristotle was the

product of activities directed towards clearly defined goals

which inform our whole life rather than being simply short-term

(Chang, Killingworth, & Noaln., 1997).

Self-report rating scales are one of the most common

methods to assess overall SWB. Sandvik, Diener, and Seidlitz

(1993) suggest that standard self-report measures of SWB are

adequate for most research as there is “a unitary core of

experience for well-being, which self-reports reflect to a great

extent. Thus, researchers using standard well-being scales can

generally expect to obtain meaningful, interpretable information

from these scales under ordinary conditions” (p.337). This is

partly attributable to the moderate stability of SWB across

situations and over the life span (Diener & Lucas, 2000). For

example, SWB has been found to correlate 0.85 over a four-year

period (Diener, Suh, & Oishi, 1997).

According to Andrich (1978) and Guilford (1954), there are

four main reasons for the frequent use of the rating scale method

of measurement:

1. Rating scales are relatively easy for researchers to

construct and use compared with other scale formats.

2. They provide the respondent with a limited number of

response options, facilitating data registration for both the

subject and the researcher.

3. The numbering continuum provides respondents with a

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ruler upon which they can mentally gauge the intensity and/or

direction of their reactions to a statement.

4. Accuracy and reliability of one’s ability to communicate

mental maps increase with experience in using mental rulers.

Also, conceivably, the repeated use of similar formats increases

the accuracy and reliability of the measurement process. One

internalized ruler can be used to measure directions and

intensities across a variety of sentiments.

There are four major methods for constructing rating scales:

Thurstone type or equal-appearing interval scales (Thurstone &

Chave, 1929), Guttman type or cumulative scales (Guttman,

1950),Semantic differential scales (Osgood, Suci &

Tannenbaum, 1957), and Likert-type orsummated rating scales

(Likert, 1932).

The Likert-type rating scale was recently proclaimed to be

one of the most important tools in attitude and survey

measurement (Bergstrom & lunz, 1998).The use of this

measuring device in psychological and educational settings is

virtually universal. Attitudinal data in marketing and public

opinion research and many types of organizational surveys rely

heavily on the rating scale method of measurement (Green &

Rao, 1970). On a Likert or Likert-type scale generally associated

with the work of Likert (1932), respondents are presented with a

series of statements and they are asked to indicate their degree

of agreement (or disagreement) with each item. Responses are

usually made on a 5- or 7-point scale, with response categories

ranging from “strongly agree” to “strongly disagree”, or other

scale point labels referring to frequency or quality. All items are

considered to be of equal value, and response to an item is

weighed to reflect the degree of agreement or disagreement. The

scale score may be either the total number of points (over all

items) or the average of all the item scores. Since the total scale

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score is obtained by adding the scores from individual items, a

Likert scale is also referred to as a summative scale.

In light of the extensive use of rating scales, it would be also

useful to have a clear understanding of how to optimize

reliability and validity through use of the scale. The number of

rating points used on the “ruler” can vary from 2 to 100 or more.

There is a general consensus that the optimal number is from 5

to 7 points. However, the specific number of points eludes

researchers. Whether to use an even or odd number of categories

is another source of debate among practitioners (e.g., Gable &

Wolf, 1993). Cox (1980; p.408) provides the following

definition of the optimal number of rating points: “At a general

level, a scale with the optimal number of response alternatives is

refined enough to be capable of transmitting most of the

information available from respondents without being so refined

that it simply encourages response error. At that optimal

number, the ratio of meaningful or systematic variation on total

variation is maximized. At an operational level, the optimal

number depends on the purpose of the scale and, thus, the nature

of its systematic variation.”

The WHOQOL-BREF is one of the best known instruments

that has been developed for cross-cultural comparisons of

quality of life and currently it is available in more than 40

languages. The WHOQOL-BREF is a modified version of The

World Health Organization Quality of Life Instrument. The

abbreviated version contains 26 questions divided into four

domains. The WHOQOL-BREF has 26 items derived from the

WHOQOL-100. The items are rated on a 5-point Likert scale.

The four domain scores are scaled in a positive direction, with a

score range of 0-20, and with higher scores denoting higher

QOL. It also includes one facet ofoverall quality of life and

general health. These items are scaled in a positive direction,

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with a score range of 1-5, and with higher scores denoting a

better quality of life and general health.

(Fig. 1)

Figure 1

WHOQOL-BREF Questionnaire Chart

Cultural biases have been shown not to suffice to explain the

major differences in SWB between countries (Veenhoven,

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1997), but they still pose a major problem to the international

comparison of QOL data (Schimmack et al., 2002). Asians, for

instance, usually have intermediate mean ratings, with a much

narrower distribution than Westerners (Diener, Smith & Fujita.,

1995). This phenomenon has been attributed to the cultural

valuation of moderation (Diener et al., 1995). Another factor

possibly contributing to the distinctive distribution of SWB

among Asians is less individualism and the persistent closeness

of family ties. Such ways of life are characterized by increased

control, and thus tend to limit the impact of perturbations on

SWB and they affect balance, whether by buffering negative

events or by blunting positive affects.

According to their personality, living circumstances or

culture, people may vary in response to questions concerning

overall life (dis)satisfactions. Schwarz and Strack (1999) have

identified several sources of bias in (conventional) self-reported

global assessments of SWB. These include assimilation and

contrast effects, when current feelings are coloured or

discoloured by the past. Similarly, the mood of the day or events

of the moment may distort responses. In addition, responses

about well-being may be biased by social acceptability (Schwarz

and Strack, 1999).

Iranian people don’t have any tendency toward answering

some questions, because the questions are related to their sexual

relationships.

As the main aim of the current study, we were interested in

using the ability and flexibility of fuzzy systems in order to

eliminate some inappropriate questions from WHOQOL-BREF

questionnaire. .A fuzzy system was designedto diminish the

errors that causeambiguous concepts by not answering specific

questions.

Question 21 was removed from thequestionnaire by using the

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fuzzy system.We aimed to calculate this question from the

measure of the social relation dimension of the questionnaire

(DOM-3) by removing this specificallyculturally biased

question. (Fig 2)

Figure 2

The Social Dimensionof the WHOQOL-BREF

Questionnaire Chart

Fuzzy Systems and the Features:

The conclusions of psychological studies and educational

sciences are based on uncertain data at this stage and they

resulted in inaccurate fuzzy concepts (Zetenyi, 1998).

Fuzzy systems are the systems based on knowledge or rules;

they are very suitable tools for the modeling of uncertainties and

ambiguities on the basis of the Fuzzy Sets Theory (Wang,

1997).

A fuzzy inference system is a set of fuzzy input(s), fuzzy

rules and fuzzy output(s) that can receive input data accurately

and give the final output in the form of accurate numbers.

Inputs of the fuzzy inference system are the concepts that

psychological and educational researches use to explain the

output(s) (Smithson & Verkuilen, 2006).

The Deduction Process and Inference Process of the fuzzy

system have five stages:

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Fuzzification, Application of Fuzzy Operators, Conclusion,

Composition, and Defuzzification

1-Fuzzification

In this phase, we putaccurate data into the system and

determine the measure of their attachment to fuzzy sets by

membership functions. In fact, we measure the satisfaction of

(the IF) part of the rule.

2- Application of Fuzzy Operators:

Where (the IF) part is made of some statements, we use the

fuzzy operators to compose statements and determine the

conclusion of (the IF) part of the rule.

3-Inference:

At this point, we define (the THEN) part on the base of (the IF)

part. The input of inference is a number from the prior stage and

the output is a fuzzy set. This step is applied once toeach rule.

4- Composition:

At this stage, we compose different outputs of rules to each

other, (each of them is a fuzzy set) and it determines the overall

space of the fuzzy system. This stage is used once for each

output variable.

5- Defuzzification:

We estimate certainty from uncertainty at this stage. The

input of the defuzzification stage is a composed fuzzy set and

the outputof the defuzzification stage is an exact number. A

fuzzy rule consists of a set of (IF-THEN) fuzzy rules. It is the

heart of the system, because we use other implements of the

system effectively to obtain the rules.

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To analyze the psychological and social phenomena is one of

the most important abilities of the fuzzy system, the possibility

of quantitative analysis based on fuzzy rules for data that are not

exact (Smithson & Verkuilen, 2006).

In this research, we design an empirical and scientific rules

based on the capabilities of thefuzzy system with the search

table of (Wang & Mandel) input - output data which has three

input parameters: personal relations relationships, sexual

relationships, and social supports of the subjects.

We obtain these three input parameters on the basis of the

measure of psychological tests (WHOQOL-BREF), and estimate

the fuzzy output parameter from the view of social relationships,

and then comparethis conclusion with the conclusion of the

normal method.

Method

A sample of 130 voluntary participants including 30 Swedish

residents, 30 Iranians living in Sweden, and 80 Iranians living in

Iran were asked to fill out the WHOQOL-BREF questionnaire.

The MATLAB software was applied to design the fuzzy

research system by (Wang – Mandel) input-outputsearch table.

We design fuzzy systems to analyze complex psychological

tests by fuzzy (linguistic) rules and nervous networks, because

of the fuzzy rules are an effective and convenient approach

tothepairs of input-output data. The Wang-Mandel approach is

composed offuzzy (linguistic) rules and the nervous networks in

psychological tests and it makes an appropriate method fromthe

pairs of input-output data. It has five basic steps (Wang, 1997).

We design the fuzzy membership function of variables of

personal relations relationships, sexualyrelationships, social

supports of the subjects in terms of the WHOQOL-BREF

questionnaire with 90 Swedes, Iranians living in Sweden, and

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Iranians living in Iran, toestablish the questionnaire by fuzzy

sets in the form below (fig 3)( Klir,& Yuan, 1995).

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Figure 3

Membership Functions of Fuzzy Variables in the

Domainof Social Relationships (Personal Relations,

Sexualy Relations, Social Support)

Five basic steps of the Wang-Mendel method are (Wang, 1997):

1- to determine the input-output membership function and to

determine membership degree of each data

2- To attain a rule for each pair of input - output data.

3- To determine a weight and a degree for each rule. We obtain the

degree of each rule by determineof the membership degree of

components and the membership degrees of the pairs of data.

4- To choose the rule that has the maximum degree, we obtain the

number of fuzzy rules in return for the different reasonsAt this

stage we might have similar introduction of (the IF) part and

different conclusion of (the THEN) part, so we have a conflict.

In this case, to resolve the conflict, we choose the rules that have

the highest weight and degree.

5- To determine the measure of the output based on the pairs of

input data related formulas (defuzzification formulas).

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RuleBases

We use the Wang & Mendel method to design the fuzzy systems

of the research. We consider 37 rules for the fuzzy system; two

of them are mentioned below:

1. If you are very satisfied with your personal relationships, and

very satisfied with your sex relationships, and very satisfied

with your social support, then your social relationship is very

high (weight of rule is 1).


very satisfied with your sex relationships, and satisfied with

social support, then your social relationship is very high (weight

of rule is.66).

3. If you are satisfied with your personal relationships, and very

satisfied with your sex relationships, and very satisfied with

social support, then your social relationship is very high (weight

of rule is.66).


satisfied with your sex relationships, and satisfied with social

support, then your social relationship is high (weight of rule

is.66).


satisfied with your sex relationships, and satisfied with social


is.66).


very satisfiedwith your sex relationships, and neither satisfied

not dissatisfied with social support, then your social relationship

is high (weight of rule is .66).

7. If you are satisfied with your personal relationships, and

satisfiedwith your sex relationships, and very satisfied with

social support, then your social relationship is high (weight of

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rule is .66).

8. If you arevery satisfied with your personal relationships, and

very satisfied with your sex relationships, and neither satisfied

not dissatisfied with social support, then your social relationship

is high (weight of rule is .66).


satisfied with your sex relationships, and neither satisfied nor

dissatisfied with social support, then your social relationship is



satisfiedwith your sex relationships, and satisfied with social

support, then your social relationship is high (weight of rule is

1).


satisfied with your sex relationships, and neither satisfied nor




very satisfied with your sex relationships, and dissatisfied with

social support, then your social relationship is high (weight of

rule is 1).

13. If you are neither satisfied nor dissatisfied with your personal

relationships, and satisfied with your sex relationships, and

satisfied with social support, then your social relationship is



relationships, and very satisfiedwith your sex relationships, and




satisfiedwith your sex relationships, and neither satisfied

nordissatisfied with social support, then your social relationship

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is high (weight of rule is.66).

16. If you are satisfied with your personal relationships, and neither

satisfied nor dissatisfied with your sex relationships, and


high (weight of rule is .66).


satisfied with your sex relationships, and dissatisfied with social


is.66).


neither satisfied nor dissatisfied with your sex relationships,

and neither satisfied nor dissatisfied with social support, then

your social relationship is high (weight of rule is.66).


relationships, and very satisfiedwith your sex relationships, and

neither satisfied nor dissatisfied with social support, then your

social relationship is high (weight of rule is.66).


relationships, and satisfied with your sex relationships, and


high (weight of rule is.66).


relationships, and neither satisfied nor dissatisfiedwith your sex

relationships, and very satisfied with social support, then your

social relationship is high (weight of rule is.66).

22. If you are issatisfied with your personal relationships, and

satisfiedwith your sex relationships, and neither satisfied nor

dissatisfiedwith social support, then your social relationship is

high (weight of rule is.66).


relationships, and satisfiedwith your sex relationships, and


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social relationship is medium (weight of rule is .66).






relationships, and neither satisfied nor dissatisfied with your

sex relationships, and satisfied with social support, then your



dissatisfiedwith your sex relationships, and satisfied with social

support, then your social relationship is medium (weight of rule

is .66).


satisfied with your sex relationships, and very dissatisfied with

social support, then your social relationship is medium (weight

of rule is 1).

28. If you areneither satisfied nor dissatisfied with your personal

relationsrelationships, and neither satisfied nor dissatisfied with

your sex relationships, and neither satisfied nor dissatisfied

with social support, then your social relationship is medium

(weight of rule is 1).




medium (weight of rule is 1).


relationships, and neither satisfied nor dissatisfied with your

sex relationships, and dissatisfied with social support, then your



relationships, and dissatisfied with your sex relationships, and

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low (weight of rule is.66).

32. If you are dissatisfied with your personal relationships, and

dissatisfied with your sex relationships, and dissatisfied with

social support, then your social relationship is low (weight of

rule is 1).

33. If you are dissatisfied with your personal relationships, and very

dissatisfied with your sex relationships, and dissatisfied with

social support, then your social relationship is low (weight of

rule is .66).

34. If you are very dissatisfied with your personal relationships,

andvery dissatisfied with your sex relationships, and very


very low (weight of rule is 1).

35. If you are very dissatisfied with your personal relationships, and

dissatisfied with your sex relationships, and very dissatisfied

with social support, then your social relationship is very low

(weight of rule is .66).

36. If you are very dissatisfied with your personal relationships, and

very dissatisfied with your sex relationships, and dissatisfied

with social support, then your social relationship is very low


37. If you are dissatisfied with your personal relationships, and very

dissatisfied with your sex relationships, andvery dissatisfied

with social support, and then your social relationship is very low


Inference

The true value of the hypothesis is one of the rules of

calculation, and the true value of the conclusion is one of the

applied rules. These conclusions are especially for the output

variable of each rule in a fuzzy subset.The rule ofthe MIN

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Inference or rule of Multiplication Inference are often used as

the Inference rule. In MIN Inference, membership function of

the output is a section of height, we calculate it by the real

degree of (the If) parts of the given rules (rule weight, α). In the

Multiple Inference, we measure and calculate the membership

function of output by the real degree of (the If) parts of rules.

Composition

There are some fuzzy subsets for each output variable; all of

these variables composing together apply as a single fuzzy

subset for each output variable. MAX or SUM isusually used for

the Composition.In MAX Composition, we compose fuzzy

subsets of outputs according to the reasonable maximum point

which is made especially considering Inference rules of all fuzzy

subsets.

In SUM Composition, we compose fuzzy subsets of outputs

according to allof the reasonable points which aremade

especially considering Inference rules of all fuzzy subsets.

DeFuzzifier

Sometimes it is useful to review fuzzy subsets which are the

conclusion of the composition process, but sometimes is

necessary changing the fuzzy measure to the more clear

measure. The defuzzification process does this stage. Two of the

most common techniques for the parameters are the Center of

Gravity and the Maximum Method.In the Center of Gravity

method, we calculate the clarityvalue of the output variable by

finding the measure of the variable from the center of gravity of

the membership function of the fuzzy value.

In the Maximum method, we calculate the clarityvalue of the

output variable by finding the measure of a variable which has

the fuzzy subsets with the maximum value of clarity.

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In this research, we use the product method for Inference,

SUM method for composition, and the Center of Gravity

method for DeFuzzifier.

Mathematical Calculation of Example

We design a fuzzy set in the fuzzy system, and we calculate

the measure of the social relationships for this data: Q22=5 and

Q20=2, so we have DOM-3=16.

0.66( 12) / 4 12 16

( ) 0.66( 20) / 4 16 20

0

y y

fuzzy y y y

otherwise

16 20

12 16

0.66( ) ( 12) ( 20) 2.64

4Area f y dy y dy y dy

16 20

2 2

12 16

0.66( ) ( 12 ) ( 20 ) 42.24

4Moment yf y dy y y dy y y dy

( ) 42.2416

2.64( )

yf y dyMomentCentroid

Area f y dy

We obtain similar conclusions for the other inputs with different

outputs of the fuzzy sets [8].

4. Discussion and conclusions:

We demonstrate the obtained conclusions from raw scores with

and without the fuzzy method (normal method) in Table 1:

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Table 1

Calculation Results areSocialRangeof 50 Subjects (Healthy and

Sick) No Fuzzy Method (Conventional and the Questionnaire

WHOQOL-BREF) and Using Fuzzy Techniques (Output Fuzzy

System Design).

N Gensiat Q20 Q21 Q22

Dom-3

(Social

Relationships)

Without Fuzzy

Dom-3

(Social

Relationships)

With Fuzzy

1 2 5 5 5 20.00 18.70

2 1 5 5 4 18.67 18.60

3 1 4 5 4 17.33 16.00

4 2 5 5 3 17.33 16.00

5 1 4 4 5 17.33 13.90

6 2 5 5 3 17.33 16.00

7 1 5 4 4 17.33 16.00

8 1 4 5 4 17.33 16.00

9 2 5 3 5 17.33 16.00

10 1 4 5 4 17.33 16.00

11 2 4 5 4 17.33 16.00

12 1 4 4 5 17.33 13.90

13 1 4 5 3 16.00 16.00

14 1 5 5 2 16.00 16.00

15 2 3 4 5 16.00 16.00

16 2 4 5 3 16.00 16.00

17 1 4 4 4 16.00 16.00

18 2 4 5 3 16.00 16.00

19 2 3 5 4 16.00 16.00

20 1 4 3 4 14.67 16.00

21 2 4 4 3 14.67 16.00

22 2 4 5 2 14.67 16.00

23 1 4 4 3 14.67 16.00

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24 2 5 3 3 14.67 16.00

25 1 4 4 3 14.67 16.00

26 1 4 3 4 14.67 16.00

27 2 4 4 3 14.67 16.00

28 2 3 4 4 14.67 16.00

29 2 3 3 5 14.67 16.00

30 1 2 4 5 14.67 16.00

31 2 4 4 3 14.67 16.00

32 1 4 3 4 14.67 16.00

33 2 4 4 3 14.67 16.00

34 1 4 3 4 14.67 16.00

35 2 3 3 5 14.67 16.00

36 1 4 4 3 14.67 16.00

37 2 3 4 3 13.33 12.00

38 1 4 3 3 13.33 12.00

39 2 4 3 3 13.33 12.00

40 1 4 3 3 13.33 12.00

41 2 3 3 4 13.33 12.00

42 2 4 3 3 13.33 12.00

43 2 4 4 1 12.00 12.00

44 2 3 3 3 12.00 12.00

45 1 4 3 2 12.00 12.00

46 1 4 3 2 12.00 12.00

47 1 3 3 2 10.67 12.00

48 1 3 2 2 9.33 8.00

49 2 1 1 2 5.33 5.40

50 2 2 1 1 5.33 5.40

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Figure 4

Graph comparing the Social Idomain without Using Fuzzy

Techniques (Conventional) Using Fuzzy Technique for 50

Students

Table 6 shows the predictable mean and standard deviation of

scores of the quality of life with a view to social relationships

through the fuzzy method. They are based on two parameters:

personal relationships, and social supports, they have

anoticeable reduction. We compare the means by the related

samples of t-test; they are presented in Table 3.

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Table 2

Comparison of the Results of a Questionnaire

WHOQOL-BREF Social Domain with and without

Using Fuzzy

Scores N Mean

Std.

Deviation

Social relations domainofthe

WHOQOL-Brief without using

the fuzzymethod

50 14.64 2.80

Social relations domainofthe

WHOQOL-Brief with usingthe

fuzzymethod

50 14.55 2.79

Table3

Ttest forPairedSamples(Dependent)

Sig. (2-tailed) df t

.659 49 .444

We demonstrate that we can remove question number 21

fromthe questionnaire, according to the rules of the Wang-

Mandel method, and we design a special fuzzy system.There is

no meaningful difference between the mean of the scores before

fuzzification and after fuzzification statistically in which 95%

isn’t reliable. It is a powerful system, because it can estimate the

conclusions of the test questions that are predictable even if

some questions are removed.

We show the standard deviation of the scores after

fuzzification is 2.79, and the standard deviation of the scores by

the conventional non-fuzzy method (normal method) is 2.80, so

we have a little reduction from some annoying latent variables

or parameters among the subjects.

The outstanding advantage of this fuzzy method is that the

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normal method collects irrelevant variables largely, and then it

cannot control predictable scores accurately.

Our analysis shows that the fuzzy system can be inference

reasonably [10]. We predict and conclude the social dimension

in the questionnaire of the fuzzy systems by two input variables

(Table 4) instead of three input variables, without using sexual

scales. This is the unique feature of fuzzy logic.

We use fuzzy logic in research on human behavior because

there are many uncertain data from psychological tests in real

situations.

Uncertainty in related data leads to obtaining inaccurate

concepts. We use fuzzy data instead of raw data, so we are able

to reduce uncertainty. In this research we suggest a new

dimension of the capability of fuzzy systems in educational and

psychological researches. The major advantage of this modeling

is that it predicts psychological parameters by measuring

uncertainty and replacing it with a quantitative measure of

ambiguity.

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Received: 3/ 12/ 2013 Revised : 21/ 6/ 2015 Accepted: 5/ 7/ 2015

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